Well, she's married, so that part is a done deal. At the base level of what she needs to do, she needs to be honest.

The name change is a minor issue. If she has a new passport with her new name, she can enter the U.S. by bringing with her both passports -- the visa in her old passport is still valid.

As for her intent to immigrate, marrying a LPR could raise questions; she should be prepared to show her continuing, strong ties to her nation of origin, and be prepared to answer questions about her future plans. If in fact she plans to immigrate, it would be sensible to discuss her situation with an immigration lawyer before she travels out of the United States.